Nonlinear PDEs appearing in fluid mechanics often have a convection term, whose role is not well-understood in my viewpoint. I want to state some problems which I cannot answer and wish to usher in young people who may solve them. A key theme is that the convection term prevents the solution from blowing-up. I want to demonstrate this `proposition' by examples.

The video for this talk should appear here if JavaScript is enabled.If it doesn't, something may have gone wrong with our embedded player.We'll get it fixed as soon as possible.